Rydberg's Constant: Diff. between R∞ & R_H

[M. next]

What is the difference between R∞ and R_{H}? Physically and mathematically.
Thanks

 

[mathman]

http://en.wikipedia.org/wiki/Rydberg_constant

Looks like they are the same.

 

[DrClaude]

What is the difference between R∞ and R_{H}? Physically and mathematically.
Thanks

R_\infty is calculated assuming a fixed nucleus (thus assuming an infinite mass), while R_\mathrm{H} is calculated for an actual proton that can move (thus in the center-of-mass frame).

In any equation where an infinite mass of the proton was assumed, you only need to replace the mass of the electron with the reduced mass of the electron+proton system to get the correct value ("correct" in the sense that you are not making the approximation that the proton cannot move).

 

[M. next]

Thank you a LOT! Sorry it took me time to recheck this thread. I would just like to know one more thing:why is it that a fixed nucleus implies an infinite mass?

 

[jtbell]

Turn it the other way around: an infinite-mass nucleus would be "fixed" as far as the atom's internal behavior is concerned.

If the nucleus and electron had the same mass (e.g. if we used a positron instead of a proton in hydrogen... look up positronium), they would both "revolve" around a point halfway between them, the center of mass of the system. (Of course this is a quantum-mechanical system so they don't revolve in the usual sense, but there is an analogous effect.)

As the mass of the nucleus increases relative to the electron, the center of mass shifts closer to the nucleus. In the limit as the mass of the nucleus goes to infinity, the center of mass approaches the center of the nucleus, in which case the nucleus wouldn't revolve at all.

 

[M. next]

Oh my! That was a great answer! Thanks